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A Simple Way for Determining the Normalized Potentials for Harmonic Maps

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Abstract

We give a simple way for determining the normalized potentials in the Weierstrass type representation of the harmonic maps for a Riemann surface to a compact symmetric space. As an application, the normalized potential for an arbitrary constant mean curvature surface in space is obtained.

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References

  1. Bobenko, A.: Constant mean curvature surfaces and integrable equations, Russian Math. Surveys 46 (1991), 1–45.

    Google Scholar 

  2. Dorfmeister, J. and Haak, G.: Meromorphic potentials and smooth CMC-surfaces, Math. Z., to appear.

  3. Dorfmeister, J., McIntosh, I., Pedit, F. and Wu, H.: On the meromorphic potential for a harmonic surface in a k-symmetric space, Manuscripta Math. 92 (1997), 143–152.

    Google Scholar 

  4. Dorfmeister, J., Pedit, F. and Wu, H.: Weierstrass-type representation of harmonic maps into symmetric spaces, Comm. Anal. & Geom., to appear.

  5. Pinkall, U. and Sterling, I.: On the classification of constant mean curvature tori, Ann. of Math. 130 (1989), 407–451.

    Google Scholar 

  6. Ruh, E. A. and Vilms, J.: The tension field of the Gauss map, Trans. Amer. Math. Soc. 149 (1970), 569–573.

    Google Scholar 

  7. Wu, H.: On the dressing action of loop groups on constant mean curvature surfaces, Tôhoku Math. J. 49 (1997), 599–621.

    Google Scholar 

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Wu, H. A Simple Way for Determining the Normalized Potentials for Harmonic Maps. Annals of Global Analysis and Geometry 17, 189–199 (1999). https://doi.org/10.1023/A:1006556302766

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  • DOI: https://doi.org/10.1023/A:1006556302766

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